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Galerkin Method for the Scattering Problem of a Slit

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Abstract

In this paper, the scattering problem of a slit is considered. By use of the exact Dirichlet-to-Neumann map and the continuity of the total field on the slit, we reformulate this problem to an operator equation. The well-posedness of the solution is proved. We apply Galerkin method to solve this operator equation numerically and prove the convergence of the numerical solution. Finally some computational examples are presented to show the effectiveness of our method.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, China

    Yujie Wang & Fuming Ma

  2. Department of Mathematics, Dalian Maritime University, Dalian, 116026, China

    Enxi Zheng

Authors
  1. Yujie Wang
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  2. Fuming Ma
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  3. Enxi Zheng
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Corresponding author

Correspondence to Yujie Wang.

Additional information

The research was supported by the National Natural Science Foundation of China (NSFC 11371172, 11271159) and the TianYuan Special Funds of the National Natural Science Foundation of China (NSFC 11526043).

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Wang, Y., Ma, F. & Zheng, E. Galerkin Method for the Scattering Problem of a Slit. J Sci Comput 70, 192–209 (2017). https://doi.org/10.1007/s10915-016-0248-z

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  • DOI: https://doi.org/10.1007/s10915-016-0248-z

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